Investigation on drag reduction on rotating blade surfaces with microtextures

To enhance the aerodynamic performance of aero engine blades, simulations and experiments regarding microtextures to reduce the flow loss on the blade surfaces were carried out. First, based on the axisymmetric characteristics of the impeller, a new simulation method was proposed to determine the aerodynamic parameters of the blade model through the comparison of flow field characteristics and simulation results. Second, the placement position and geometrical parameters (height, width, and spacing) of microtextures with lower energy loss were determined by our simulation of microtextures on the blade surface, and the drag reduction mechanism was analyzed. Triangular ribs with a height of 0.2 mm, a width of 0.3 mm, and a spacing of 0.2 mm exhibited the best drag reduction, reducing the energy loss coefficient and drag by 1.45% and 1.31% for a single blade, respectively. Finally, the blades with the optimal microtexture parameters were tested in the wind tunnel. The experimental results showed that the microtexture decreased energy loss by 3.7% for a single blade under 57° angle of attack and 136.24 m/s, which was favorable regarding the drag reduction performance of the impeller with 45 blades.


Boundary layer theory
As shown in Figure 1, the fluid near the wall at the front end of the flat plate is laminar.However, the flow in the boundary layer will gradually transform to turbulent as the fluid flows along the flat plate.This transformation occurs gradually, and there is no distinct boundary line between the laminar and turbulent flow regions.The near-wall region within the boundary layer is the primary source of turbulent kinetic energy.This region can be divided into three distinct regions, namely, the viscous sublayer, the buffer layer, and the turbulent region (log-law region) [1].The position of each region within the boundary layer is determined based on the dimensionless normal distance from the wall [2][3][4]: where y is the distance from the wall, uτ is the wall stress shear velocity, and v is the kinematic viscosity of the fluid [5].According to Figure 2, the near-wall

S3
area is usually in the range of y + ≤ 100.The range of the viscous sublayer region is 0 ≤ y + ≤ 5; here, the viscous shear stress is dominant, and the turbulent shear stress is zero.The buffer layer is 5 ≤ y + ≤ 30, characterized by the simultaneous presence of both viscous and turbulent shear stresses.The overlap layer ranges from 30 ≤ y + ≤ 100, where the turbulent shear stress becomes dominant [6].

Drag reduction formulas
The total resistance (F) of the blade is mainly composed of two parts, that is, pressure drag (Fp), caused by the pressure gradient, and frictional drag (Ff), caused by the viscous of the wall.Their relationship is as follows: where Cf is the friction coefficient of the microstructure, Af is the surface area of the object, ρ is the density of the fluid, and u0 is the velocity of the fluid.Thus, the drag reduction rate (DRR) of the blade surface can be expressed as: where F0 and F1 are the total resistance on the smooth blade and microtextured blade, respectively.Then the change rate of energy loss coefficient (ηξ) and S5 total pressure loss coefficient (LCTP) are used to represent the change of resistance of the blade and flow path to improve the reliability of the results [9]: where ξ0 and ξ1 are the energy loss coefficient of the smooth blade and microtextured blade, respectively.The energy loss coefficient (ξ) is defined as: where SI and SA are the static enthalpy of the isentropic process and actual process, respectively; TP1 and TP2 are the total pressure on the inlet and outlet of the impeller flow path, respectively; P1 and P2 are the static pressure on the inlet and outlet of the impeller flow path, respectively; k is the specific heat ratio and, for air, it is 1.4.LCTP can be expressed as: TP is equal to the sum of dynamic pressure (DP) and P, which can be calculated by the following equation: where Ma is the Mach number; Ma is defined as: where V is the airflow velocity, and the speed of sound, C, is defined as: where T is absolute temperature, and R is the specific gas constant.In this paper, the value of T and R are 300 K and 287 J⋅kg −1 ⋅K −1 , respectively.S6 ηξ represents the change of energy consumption of the whole system.A higher ηξ indicates an increase of energy consumption of the system, indicating that microtexture has an adverse effect on the aerodynamic performance of the blade.

Flow separation on the blade surface
The blade is a curved surface with a complicated flow situation, and flow separation occurs at high-speed air flow over the blade.Figure 3

Figure S1 :
Figure S1: Development of the boundary layer on near wall surface.

Figure S2 :
Figure S2: The range of y + corresponding to each region in the boundary layer.
shows the schematic of flow around the airfoil surface, where point A is the stagnation point, point B is the highest point, and point C is the flow separation point.The region between A and B is the pressure surface, characterized by smooth airflow along the wall without boundary layer separation.Therefore, this region is discretized and treated as a collection of small local planes.The region between B and C is the suction surface where the flow surface increases, causing the outflow to decelerate, the pressure to rise, and the kinetic energy to be converted into pressure energy.Conversely, the pressure difference behind point C triggers flow reversal and separation of the boundary layer from the wall, resulting in a vortex zone known as the separation region.The generation of the separation region significantly impacts the outflow boundary, thereby relieving the influence of viscosity on the thin fluid layer near the wall.

Figure S3 :
Figure S3: The schematic diagram of boundary layer separation on airfoil